arXiv subjects

Jake McNaughton

Publications and source records attributed to Jake McNaughton.

3 recordsLinked to original sources

arXiv2025

Full-Precision and Ternarised Neural Networks with Tunnel-Diode Activation Functions: Computing and Physics Perspectives

The mathematical complexity and high dimensionality of neural networks slow both training and deployment, demanding heavy computational resources. This has driven the search for alternative architectures built from novel components, including new activation functions. Taking a different approach from state-of-the-art neural and neuromorphic computational systems, we employ the current-voltage characteristic of a tunnel diode as a quantum physics-based activation function for deep networks. This tunnel-diode activation function (TDAF) outperforms standard activations in deep architectures, delivering lower loss and higher accuracy in both training and evaluation. We also highlight its promise for implementation in electronic hardware aimed at neuromorphic, ternarised and energy efficient AI systems. Speaking broadly, our work lays a solid foundation for a new bridge between machine learning, semiconductor electronics and quantum physics -- bringing together quantum tunnelling, a phenomenon recognised in six Nobel Prizes (including the 2025 award), and contemporary AI research.

physics.app-ph↗

arXiv2025

Adaptive Neural Quantum States: A Recurrent Neural Network Perspective

Neural-network quantum states (NQS) are powerful neural-network ansätzes that have emerged as promising tools for studying quantum many-body physics through the lens of the variational principle. These architectures are known to be systematically improvable by increasing the number of parameters. Here we demonstrate an Adaptive scheme to optimize NQSs, through the example of recurrent neural networks (RNN), using a fraction of the computation cost while reducing training fluctuations and improving the quality of variational calculations targeting ground states of prototypical models in one- and two-spatial dimensions. This Adaptive technique reduces the computational cost through training small RNNs and reusing them to initialize larger RNNs. This work opens up the possibility for optimizing graphical processing unit (GPU) resources deployed in large-scale NQS simulations.

cond-mat.dis-nn↗

arXiv2024

Projective Geometry and PDE Prolongation

In this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary differential equation into n first order equations. For partial differential equations there is a related process but it is far more subtle and complex. Considerable work has been done in this area but much of this is very abstract and there are many open problems even at a relatively elementary level. We introduce the reader to differential geometry and tractor calculus before recovering the projective tractor and cotractor connections via the prolongation of appropriate partial differential equations. Following this, we study prolongation of other projectively invariant equations, a particular focus is an equation known as the projective metrisability equation.

math.DG↗